Working out the expansion in powers of \(\gamma \)  or \(\alpha \)  for \(V_0\) , one has that \(V_0=-2\pi \alpha \gamma _E/p^2+{\cal O}(\alpha ^3)\) , in agreement with our perturbative calculation of \(V_0^{(1)}\)  and \(V_0^{(2)}=0\) , fixing then \(\ln a=\gamma _E=0.577\) . There is another way to fix \(\ln a\)  by using the known asymptotic behavior of the Coulomb wave functions, which was considered in Ref. [1]}. Within the small angle approximation to all orders in \(\alpha \) , Ref. [2]} in QED also obtains the extra phase \(-2\gamma (\log \mu +\gamma _E)\)  of \(S_c\) .
